Mathematical game



Feb. 3, 1959 G. P. GuzAK MATHEMATICAL GAME 2 Sheets-Sheet 1 Filed Aug.l. 1956 n, R S m \m\/ W. v NQ TS g wm ,8f mv wm wm S NN 10M QQ MIR Ni mTmm .QQ n@ w3 wm MQ 0l. W NQ $4 \mm .QQ ww .om n. Nw. 2 M NQ 5 QQ mN- Qww .QE v N NN` lv QS or o2 @n QQ ow om Sv om. QN S s Wd W ma u" S I ENn" u" S mmPfl. n mm am umllo@ um wm ma m m QQ E 2 h2 3.1;: NS QS ma. Nmmm wm, QQ NN. ,.vm wl, mJv Rv Nm. .WN s m. w wm .wm vm mw Nm R. mm ma mwy ww .um vm om d ,wm Nw um mw S /M vw mn n av on ma un wn nu ma j M wmwm ,9 o@ Sv uw wm on vw m4 S o w .U h n@ Ww mw Ww QNGW |||Ww mw NW xw umhh Pn mw Sv hm om nm/. .mm vm E S .o m ou n. n. wh .R N. hn z: n mv TNWmw wv @.v wm Nm .uw vw @NV S v v 3v v u bv v mv Nv :v 3. an mm m mm. mmQn N vm 4. S m m Mr Q WM Ihm 6M Mm. Nm R. om WN NN AN x .N Y MN ww uwQwh NQ S .Q` w av N N Y MN N |||DNT L s Q S S m my n m h 9v n w VBA\W\.\NNJ b\ h 0 |W sv M. N N\ Q E. m w n v n. N h

Feb. 3, 1959 G. P. GUzAK MATHEMATICAL GAMEv 2 sheets-sheet 2 Filed Aug.l, 1956 United States Patent MATHEMATICAL GAME` George P. Guzak,Chicago, Ill. Application August 1, 1956, lserai No. 601,521

Claims. (Cl. 3S-31) 'This invention pertains to a novel mathematicalgame and more particularly pertains to a game intended to teach themultiplication tables.

It is well known that teaching mathematicsV to childrenv tions of themultiplication tables` to children of grammar school age. I.

lt is a still further object of this invention to provide a mathematicalgame which maybe played by any nurnber of children and a game in whichthe children who are onlookers will, as a matter of course, mentallyperform the mathematical gymnastics required by the child playing at anyone instant.

The above and other objects of this invention will become more apparentupon proceeding with the following detailed description when read vinthe light of, the accompanying drawings and appended claims.

In one embodiment of this invention a game board is provided which ispreferably rectangular in configuration. A consecutive series ofnumerals is disposed along one edge thereof and a second set of numeralsis disposed along a second edge of the game board which intersects withthe first-mentioned edge. The two series of numerals commence at thecorner of numeral intersection of the game board and progressivelyincrease as they proceed away therefrom. Disposed normally to leachnumber of each group is a game board column. Consequently at theintersection of two columns disposed normally to a number in each of thetwo above-mentioned groups, a square will be defined. Appearing in eachof these squares is the numerical product of the two numbers with whichthe square is in alignment. It is thus apparent that the game boardcomprises a-pl'urality of squares in .alignment with numbers in twoseries disposed along the game board edges. In each square the productof the4 two numbers with which the square is in alignment is disclosedtherein.

Game pieces to be utilized in conjunction with the above-described gameboard comprise blocks having an upper inclined surface on which aredisposed a multiplier and a multiplicand. On the bottom surface of thegame piece, whichsurface is hidden from View, is printed the product ofthe multiplier and multiplicand disposed on the upper visible surface ofthe game piece. Each game piece is positioned on a square of the gameboard having a product disclosed in the square which is identical withthe product found on the game piece bottom surface,

.the other series 16 as a series of multiplicands.

also be noted that each of the series commences at the e ce Also used inconjunction with the game board are means which indicate to the playerwhich game piece is to be removed from the game board. Such means maycomprise two die members which .are thrown by the player. The twonumbers which face up after the throw direct the player to the gamepiece on the game board having the identical numbers disclosed on itsupper surface. It is the object of the game for the player, once he isconfronted with a given multiplier and multiplicand, to give the productof the same. Consequently, after the player has thrown the dice he willlook at the board, pick out the game piece having an identicalmultiplier and multiplicand, and before he moves the piece from theboard state the product of the twol numbers. The player and all who playwith him will readily find vthe correct product, if not kno-wn,` of themultiplier and multiplicand by removing the game piecev from the board.The product will be found on the game board and on the bottom surface ofthe game piece. Obviously the product need not be on both the game pieceand board; thus the game piece bottom surfaces may be blank if desired.

The number of turns each player may have is a matter:

of choice, and thegame is won by giving the greatest number of correctanswers.

For a more complete understanding of this invention reference should nowbe had to the drawings, wherein:

. Figure l is a plan view of the game boardt-o be utilized in thesubject invention;

Fig. 2 is a plan view of a means for determining a multiplier andmultiplicand to be used by a player playing thesubject game; p

Fig. 3 is a fragmentary side elevational view of the game board of Fig.1 having disposed thereon game pieces which are utilize/d in conjunctiontherewith;

Fig. 4 is a front perspective view of a game piece to be utilized withthe subject game; v v

Fig. 5 is a bottom perspective view of the game piece of'Fig. 4; v,

Fig. 6 is a perspective view of a twelve-sided die mem ber which is an,alternate means for determining a multiplier and multiplicand;

. Fig. 7. is a perspective view of a six-sided die member which maybeutilized for determining `a multiplier or a multiplicand between 1 to 6;n

Fig. 8 is a fragmentary elevational view taken on line 8 8 of Fig. 2;

Fig. 9 is a perspective View of a six-sided die` member which may be`utilized for determining a multiplier or multiplicand between 9 through12, and

Fig. 10 is a perspective view of avsiX-sided die member which may beutilized for determining a multiplier or multiplicand between 4 through9.

Referring now more particularly to Fig. l, a game board 10 isillustrated which is of rectangular configuration and which has a seriesof consecutive members running from l to 12 arranged along its upperlongitudinal edge and which has a second series of numbers from l tol2-arrangeal along theV left side-defining edge. One series 14 may beconstrued as a series of multipliers, and It will corner ofintersection, that is, at the upper left-hand cornerof the game boardillustrated.

Normally disposed to each number in each series is a column defined bythe lines 12 or 13 which run the length and width ofthe board,respectively. -It is apparent that the column lines 13 disposed normallyto the multipliers 14 disposed along the top longitudinal edge of thegame board 10 upon intersecting with the column lines 12 disposednormally to the multiplicand numerals 16 disposed along the leftside-defining edge of the board willy form squares which are uniformlydistributed over the entirey board surface. `On each of the squares aproduct is printed which corresponds to the productorthe multiplier andmultiplicand with which the particular square is in alignment. lt is'thus apparent that tjtlie'int'e'rseotin of columns drawn normally to amultiplierv a'nd"a"m.tlti' plicand a product will be readily' foundon'tlie`r gameboa'rd'- surface. Although each' of the' series l" andE leareillus'.l

trated as running from l to l2,` it is apparent that' "elength of eachseries may be as short or as long as desired.'

lt is intended in the normal courseV of play that game pieces suchV asis illustrated in Figs. 4 and 5 be utilized in' conjunction with thegame ooard lil. Each game piece ld may be somewhat' wedge-like in'configuration and hasr view. Game piece 18' willalso be arranged on thegame board lil-in such am'anner so that the multiplier and multiplicandwill' be facing the player and readily seen by him.

Prelim'inarily toVcommencing-play with the provided game,- eachl of thesquaresof the game board 1G illustrated in Fig. l has positioned thereona game piece i8. Two game pieces are shown in Vplace on the board lil inFig. l. Each game piece will have printed on its upper inclined surface18a ay multiplier and multiplicand which corresponds with the multiplierand multiplicand with which the square on whichthe game piece ispositioned is in alignment. r Torfacilitate the initial disposition of#the various game pieces 18 on their proper game hoard squares',- eachsquare of the game board'has a position number nl printed in its upperleft-hand'corner, and each game piece 18' has a`correspondingp'osit'ionnumber nrv in the upper left-hand corner of itsupper inclined surface 18a; -Thus to prepare the game board and the gamepieces for play, the number of the game piece 'is checked with acorresponding position number on the 'game board lll, thereby tofacilitate preparation of the hoard and piecesfor play.

Means may be utilized. which will iixedly position each game piece onits'pro'per game board square. For instance, projecting studs Ztl may beformed integrally with the bottom surface ldb of ea'chvgame piece 18;These studs arev intended to interlockwith the apertures 22 which may bepositioned in each square of the game board l as illustrated in thesquare fS- illustrated in Fig. l. It is believed obvious in viewof theVforegoingd escription that the game piece 1S illustrated in Figs. 4.and5 wouldr be. properly locked in square 4l of the game board in thenormal playing position.v

It is the object of this game to present vthe children who are` engagedin playing the same with a multiplier and multiplicand. The child mustthen substantially instantaneously give the product of the two numbers.With the game board illustrated in Fig, l, the child whose .turn itis inthe game may be ypresented with la multiplier ainda multiplicand, eachof which may range from l to l2.v Assuming that ythe child was.presented with afmultiplierA and a multiplicand 5, he would glance atthe lgame board (Fig. l) on which the game pieces 18 illustrated inFigs. 4 and 5 would be placed. A side elevation of sucha board and gamepiece assembly/is illustrated in Fig. 3. To nd the appropriate gamepiece, that is, the game'piece pertaining to his problem, the childwould V'glance along the top edge of the game board illustrated in Fig.;l until he. had visually located the multiplier d and would then glancealong the left side-definingedge of the game board until themultiplicand 5 was located. `Wheretljlecolumns. n ormally disposed tothese two numeralsiintersect, the perti- Each game piece i8 hasl nentgame piece wouldbe positioned. This would be the gamelpiece-illustrated*in-Fig; 4. rlhe multiplier and multi.

l to the rules of the game, if the child has correctly answered hisproblem in multiplication he may either be given another chance or elsegivenl credit for his correct answer and play will continue with anotherchild in the group.

Means are provided for use in conjunction with the illustrated gameboard 10 and gaine pieces 18 for providing the child with a randommultiplier and multiplicand. Such means may comprise the spinner board22 illustrated in Fig. 2. On the spinner board are disposed two dialmem-bers 24 and 24a. Each of the dial members comprisesa series ofconcentricy rings 26, and each ring is in turn divided into segments 2Sin which o-ne number is disposed.Y Rotat'ably mountedin the center ofeach dial 24'ar1dv 24a are spinner members 3d. As illustrated in Fig'.2, the two spinner' members project from the center of the' dial onwhich they are rotatably mounted solas to mutually overlap when directedtoward each other. To simultaneously rotate the two spinner'members .Siltheyl are merely spun with a fingernail in a manner which will iriipa'rtrotational movement to the two spinners. lt will be notedfrom Fig; 8that each member Sh spins freely since there is a clearance between thevtwo spinner members in the' vertical plane. After the two spinners 30have come to rest, one numeralfrom' each dial is presented to the child.playing the game.- The numeral from the lirst` dial 24 may be amultiplier and that from the dial 24:12

may be multiplicand;

The ring 26 of each'dial'lzu laiuti-:1.4:which 'is to be nti--y lized inthe presentation 'of' the multiplier 'and multiplicandY to thez'child'engag'ed'in the gaine will depend upon his'age and 'mathematicalability. For instance, if a child has just started ot learn themultiplication table'sthe innermost `ring of 'the illustrated dial willbe utilized with the spinnermembers 30. Consequently the child'cannot beconfronted with a multiplier and multiplicand which exf ceeds 6.However, as the child progresses in age and in ability, another ring 26of the 'illustrated dials 24 and 12451 will be utilized in vobtaining alrn'l'il'ti'plie'r vand multiplicand. Thus, if the second ring of theillustrated dial is utilized with the spinner members 30, the multiplierand multiplicand'whicha child will receive in the course of the gamewill run from 4'through 9. If 'the third outermost ring yof theillustrated dial members is utilized the vmultiplier and multiplicand'will run from 7 to l2, and if the outermost 'ring of the illustrateddial members is utilized the multiplier and multiplicand' maybe anynumeral from l through l2.

To facilitate 'reading 'of'the'umbe'rs in any one-ring, amovable-indicator such 'as indicators 32 which are slid'able on each ofthe 'spinner members 30 may beutili'z'ed. The indicators'32 'arepreferably colored so a's tocontra'st with' the underlying 'dia-l'member and readily yindicate to the child playin'gth'e game whichnumbers-are to be multiplied and the product'thereof given.

vIt is thus seen that in the 'normal course of 'playing the providedgame, the child may spin spinner members 30 of'the multiplier dial '24and multiplicand dial 24a illustrated. Depending upon where thespinnermembers 30 come to rest and uponwhich circle ofthe respective dials4isutilized, a multiplier and multiplicand is 'provided the child.Having been provided with the two numbers to be multiplied, the childwill refer to the game board lvof Fig. l. onfwhich the game pieces 18are disposed. Having located the.gar ne piece having the multiplierA and.multiplicand with which hehas Vbeen pro'- vided onitsu upper inclinedsurface he will "s'tate the product aloud before removing the gainepiece from the game board. If his answer is correct he will be entitledto another chance or receive a game point which will be counted toward aiinal sum which will determine the eventual winner.

An alternate means for providing children playing the subject game withrandom multipliers and multiplicands comprises twelve-sided die members,one of which is illustrated in Fig. 6. Two of these die members are tobe used simultaneously.` Upon throwing the dice the child whose turn itis in the game will be provided with a multiplier and multiplicand. Thelatter two numbers will be obtained from the die surfaces which remainuppermost after the dice have been thrown. The child then follows theabove-described procedure by referring to the game board 10, finding theappropriate game piece, and saying aloud the product before he hasremoved the game piece from the board. Dice 34 of Fig. 6 are to beutilized if the child playing the game has so advanced in hismultiplication as to lbe capable of multiplying numbers from 1 to 12.

However, if the child playing the game is young in age, dice 36, one ofwhich is illustrated in Fig. 7, which are the common six-sided dice, maybe utilized. Obviously, with the latter die members a child who hasthrown the same cannot be confronted with a multiplier or multiplicandover 6. The latter die members will still be used with the provided gameboard of Fig. 1. However, the area of the board to be used with suchdice will be only that area subtended by the multipliers andmultiplicands 1 to 6. Various segments of the multiplication tables maybe arranged on six-sided dice. For instance, in Fig. 9, numerals 7 to 12are disposed on the six sides of the illustrated die 37, and in Fig. 10numerals 4 through 9 are arranged on the six` sides of illustrated diemember 39. Learning pre-selected portions of the multiplication tablesmay be facilitated by using the various die members illustrated.

It is thus apparent that a novel game has been provided which will addinterest to the usually dull task of learning the multiplication tables.By enabling the child to play a game in the course of learning thesetables and by providing an incentive to win, it is believed that theefforts ordinarily expended by a child in the process of learning themultiplication tables will be greatly increased, and the time in whichthe tables are completely learned will be greatly shortened. Theprovided game, as is above apparent, is composed of a number ofinexpensive parts which may be composed of wood, plastic, and otherordinary inexpensive material. The Imanufacture of the game componentsmay be readily effected in a facile manner.

As has been above mentioned, substitute parts may be utilized in thegame which will function to equal advantage. For instance, any number ofmeans may be utilized which will provide a child with a randommultiplier and lmultiplicand. Three of such means have been abovedescribed. Also, as previously mentioned, the products of the variousmultipliers and multiplicands need not be disposed on both the gameboard and game piece bottom surfaces but may be disposed on either gameitem. It is intended, therefore, that this invention be limited only bythe scope of the appended claims.

I claim:

1. A mathematical game comprising a rectangular game board, a series ofnumbers arranged along two intersecting edges of said game board, eachof said series commencing at said intersecting corner, said game boardbeing divided into a number of squares, each of said squares being inalignment with a number from each of said series arranged along saidgame board edges, removable garne pieces positioned on each of said gameboard squares, and means for providing by chance two numbers arrangedalong the edges of said game board whereby the players of the game are'required to locate 6 the square on the game board in alignment with thetwo numbers on the edges provided by chance prior to removal of the gamepiece therefrom.

2. A mathematical game comprising a game board having numerals arrangedalong a first edge and numerals arranged along a second edge disposed atsubstantially right angles to said rst edge, said board having columnsthereon normally disposed to each of said numerals disposed along saidrst and second edges, said columns defining squares at points ofintersection, numbers corresponding to the product of the two numberswith which each of the intersecting columns is normally disposedpositioned in each of said squares, game pieces adapted to be positionedon each of said game board squares and. means for providing by chancetwo numbers arranged. along the edges of said game board wherebgI theplayers.

of the game are required to locate the square on the game board inalignment with the two numbers on the edges provided by chance prior toremoval of the game piece therefrom.

3. A mathematical game comprising a game board having numerals arrangedalong a first edge and numerals arranged along a second edge disposed atsubstantially right angles to said first edge, said board having columnsthereon normallydisposed to each of said numerals disposed along saidrst and second edges, lsaid columns defining squares at points ofintersection, game pieces adapted to be positioned on each of said gameboard squares, and means for providing by chance two numbers arrangedalong the edges of lsaid game board whereby the players of the game arerequired to locate the square on the game board in alignment with thetwo numbers on the edges provided by chance prior to removal of the gamepiece therefrom.

4. A mathematical game comprising a rectangular game board, a series ofnumbers arranged along two intersecting edges of said game board, saidseries commencing at said intersecting corner, said game board beingdivided into a number of squares, each of said squares being inalignment with a number from each of said series arranged along saidgame board edges, removable game pieces disposed on each of said gameboard squares, each of said game pieces having the product of the twonumbers with which the game board square on which positioned is inalignment disclosed on the bottom surface thereof, and means forproviding by chance two numbers arranged along the edges of said gameboard whereby the players of the game are required to locate the squareon the game board in alignment with the two numbers on the edgesprovided by chance prior to removal of the game piece therefrom.

5. A mathematical game comprising a rectangular game board, a series ofnumbers arranged along two intersecting edges of said game board, saidseries commencing at said intersecting corner, said game board beingdivided into a number of squares, each of said squares being inalignment with a number from each of said series arranged along saidgame board edges, removable game pieces disposed on each of said gameboard squares, each of said game pieces having the product of the twonumbers with which the game board square on which positioned is inalignment disclosed on the bottom surface thereof, each of said gamepieces having the two numbers with which the game board square on whichpositioned is in alignment disclosed on a top surface thereof, and meansfor providing by chance two numbers arranged along the edges of saidgame board whereby the players of the game are required to locate thesquare on the game board in alignment with the two numbers on the edgesprovided by chance prior to removal of the ga-me piece therefrom.

6. The game as recited in claim 5 in which the game piece surface onwhich said two numbers with which the game board square on whichpositioned is invalignment is inclined to the horizontal for purposes offacilitating 'reading'thereofinl the normal courseof play.

7L A' mathematical game'comprisinga game'board, a series of numbersarrangedzalong twoedges of'said'board, saidl edges beingfnormally'disposed to each' other, said game 'board' beingdivided into a' numberofsquares, each of said'squares being" in' alignment with a number fromeach''of` said1 series ofv numbers, removable game pieces arranged onyeachof said'game'boardI squares,` each' of said gamepieces'havingtheproductof the two numbers with which eachL of'saidsquares* isin alignment'y disclosed'l on the bottom thereof; a' positionnumber disclosed on each ofsaid squares; a=corresponding position numberdisclosed 4on-eacl ofsaid game pieces, and 'means forlproviding'bychance two numbers arranged along the" edges of`saidgameboard'whereby the players of thegame-are requiredto'locate/thel squareon the game boardin alignmentwith'the'v two' numbers on the edgesprovided by chance prior'tofemoval'of the game piece therefrom.

8. The game as recited in claim 1 in which'said chance means `comprisestwo diemembers.

9,- Thegame as recited` in claim-1 in kwhich said chance meanscomprisestwo^numbered dial members having a spinner member axed thereto;

10. A mathematical game comprising a rectangular` game board, a seriesof multipliersl arranged along one edge of said'fboard,` al series-ofmultiplicands arranged along a secondedge of said`board, said game boardbeingldivided into a numberof squares, each of said squares being'inalignment with a number from each of said series'arrangedalong-'saidgame board edges, re-

movable game pieces positioned on each of said game boardsquare's,Aeach'offsaid squares having two numbers*--` disclosed thereon,said`two"numbers' comprising the'num- A bers'in each ofsaidseries"disposed"along said gameboard with'which saidsquareon'whichsaid game'piece ispositioned is in alignment with, meansfor-providing by"y chance two-numbers arranged' along' the edgesv ofsaid gameboard Awherebythe' players' of' thel game are re= quiredzto'locatetthesquare'on vthe game-board in aligna ment with-the two numberson thel edges provided by cliangeprior tot'removal of" the gameV piecetherefrom, said Imeans comprising ,two'di'al-members'disposed on` arigidbacking member, a spinner member disposed on' eachof said dials,said spinner members overlappingVVV whendisposed'normalAtoth'e'adjacen't dial member, each of-'said dial m'emb'ershavngaplurality of concentric circles, each-of'said circles-'beingdividedinto a plurality of segments, numbersidispgosedineach of rsaid segments.

Rf'eferelnces GitdJ-in thele' of lthisf patent UNITED 'STATES PATENTS

